Solve the following question: a) Convert 500 cm to m. b) If the perimeter and length of the rectangle are 20…

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Solve the following question: a) Convert 500 cm to m. b) If the perimeter and length of the rectangle are 20 cm and 6 cm respectively, calculate the breadth of the rectangle. c) Find the volume of the

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Here are the solutions to the questions:

6. Solve the following question

a) Convert 500 cm to m.

Recall the conversion factor between centimeters and meters.
$1 \text{ m} = 100 \text{ cm}$
Convert 500 cm to meters.
$500 \text{ cm} = \frac{500}{100} \text{ m} = 5 \text{ m}$
The conversion is $\boxed{\text{5 m}}$ .

b) If the perimeter and length of the rectangle are 20 cm and 6 cm respectively, calculate the breadth of the rectangle.
Write the formula for the perimeter of a rectangle.
$P = 2(l + b)$
where $P$ is the perimeter, $l$ is the length, and $b$ is the breadth.
Substitute the given values ( $P = 20 \text{ cm}$ , $l = 6 \text{ cm}$ ) into the formula.
$20 = 2(6 + b)$
Solve for $b$ .
$\frac{20}{2} = 6 + b$ $10 = 6 + b$ $b = 10 - 6$ $b = 4 \text{ cm}$
The breadth of the rectangle is $\boxed{\text{4 cm}}$ .

c) Find the volume of the given cuboid.
Identify the dimensions of the cuboid from the image.
Length ( $l$ ) = 5 cm
Width ( $w$ ) = 3 cm
Height ( $h$ ) = 4 cm
Write the formula for the volume of a cuboid.
$V = l \times w \times h$
Substitute the dimensions and calculate the volume.
$V = 5 \text{ cm} \times 3 \text{ cm} \times 4 \text{ cm}$ $V = 15 \text{ cm}^2 \times 4 \text{ cm}$ $V = 60 \text{ cm}^3$
The volume of the cuboid is $\boxed{\text{60 cm}^3}$ .

7. Solve the following question

a) Write in indices: $3^2 \times 6 \times 3$ .
Express all numbers as products of their prime factors.
$6 = 2 \times 3$
Substitute the prime factors back into the expression.
$3^2 \times (2 \times 3) \times 3$
Group terms with the same base and apply the exponent rule $a^m \times a^n = a^{m+n}$ .
$2 \times 3^2 \times 3^1 \times 3^1$ $2 \times 3^{(2+1+1)}$ $2 \times 3^4$
The expression in indices is $\boxed{2 \times 3^4}$ .

b) Simplify: $8a + 6b - 4a$ .
Identify and group like terms.
$(8a - 4a) + 6b$
Combine the like terms.
$4a + 6b$
The simplified expression is $\boxed{4a + 6b}$ .

8. Solve the following question

a) Multiply: $5x \times x - 5x$ .
Perform the multiplication first.
$5x \times x = 5x^2$
Substitute the result back into the expression.
$5x^2 - 5x$
The multiplied expression is $\boxed{5x^2 - 5x}$ .

b) Divide: $20x^3 \div 4x^2y$ .
Write the division as a fraction.
$\frac{20x^3}{4x^2y}$
Divide the coefficients and apply the exponent rule $\frac{a^m}{a^n} = a^{m-n}$ for variables.
$\frac{20}{4} \times \frac{x^3}{x^2} \times \frac{1}{y}$ $5 \times x^{(3-2)} \times \frac{1}{y}$ $5x \times \frac{1}{y}$ $\frac{5x}{y}$
The result of the division is $\boxed{\frac{5x}{y}}$ .

c) 1 is a prime number. Is this statement true, false or open?
Recall the definition of a prime number.
A prime number is a natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself.
Evaluate the number 1 against this definition.
The number 1 is not greater than 1, and it only has one positive divisor (which is 1). Therefore, 1 does not fit the definition of a prime number.
The statement "1 is a prime number" is $\boxed{\text{False}}$ .

Solve the following question: a) Convert 500 cm to m. b) If the perimeter and length of the rectangle are 20 cm and 6 cm respectively, calculate the breadth of the rectangle. c) Find the volume of the

Step-by-step solution

Recall the conversion factor between centimeters and meters.

Convert 500 cm to meters.

Write the formula for the perimeter of a rectangle.

Substitute the given values ( $P = 20 \text{ cm}$ , $l = 6 \text{ cm}$ ) into the formula.

Solve for $b$ .

Identify the dimensions of the cuboid from the image.

Write the formula for the volume of a cuboid.

Substitute the dimensions and calculate the volume.

Express all numbers as products of their prime factors.

Substitute the prime factors back into the expression.

Group terms with the same base and apply the exponent rule $a^m \times a^n = a^{m+n}$ .

Identify and group like terms.

Combine the like terms.

Perform the multiplication first.

Substitute the result back into the expression.

Write the division as a fraction.

Divide the coefficients and apply the exponent rule $\frac{a^m}{a^n} = a^{m-n}$ for variables.

Recall the definition of a prime number.

Evaluate the number 1 against this definition.

Still stuck on this one?

More Mathematics Questions

Solve the following question: a) Convert 500 cm to m. b) If the perimeter and length of the rectangle are 20 cm and 6 cm respectively, calculate the breadth of the rectangle. c) Find the volume of the

Step-by-step solution

Recall the conversion factor between centimeters and meters.

Convert 500 cm to meters.

Write the formula for the perimeter of a rectangle.

Substitute the given values (P=20 cmP = 20 \text{ cm}P=20 cm, l=6 cml = 6 \text{ cm}l=6 cm) into the formula.

Solve for bbb.

Identify the dimensions of the cuboid from the image.

Write the formula for the volume of a cuboid.

Substitute the dimensions and calculate the volume.

Express all numbers as products of their prime factors.

Substitute the prime factors back into the expression.

Group terms with the same base and apply the exponent rule am×an=am+na^m \times a^n = a^{m+n}am×an=am+n.

Identify and group like terms.

Combine the like terms.

Perform the multiplication first.

Substitute the result back into the expression.

Write the division as a fraction.

Divide the coefficients and apply the exponent rule aman=am−n\frac{a^m}{a^n} = a^{m-n}anam​=am−n for variables.

Recall the definition of a prime number.

Evaluate the number 1 against this definition.

Still stuck on this one?

More Mathematics Questions

Substitute the given values ( $P = 20 \text{ cm}$ , $l = 6 \text{ cm}$ ) into the formula.

Solve for $b$ .

Group terms with the same base and apply the exponent rule $a^m \times a^n = a^{m+n}$ .

Divide the coefficients and apply the exponent rule $\frac{a^m}{a^n} = a^{m-n}$ for variables.